SLAMSH - send multiple shifts through a small (single node) matrix to see how
consecutive small subdiagonal elements are modified by subsequent shifts in an
effort to maximize the number of bulges that can be sent through
- SUBROUTINE SLAMSH
- ( S, LDS, NBULGE, JBLK, H, LDH, N, ULP )
INTEGER LDS, NBULGE, JBLK, LDH, N REAL ULP REAL S(LDS,*), H(LDH,*)
SLAMSH sends multiple shifts through a small (single node) matrix to see how
consecutive small subdiagonal elements are modified by subsequent shifts in an
effort to maximize the number of bulges that can be sent through. SLAMSH
should only be called when there are multiple shifts/bulges
(NBULGE > 1) and the first shift is starting in the middle of an
unreduced Hessenberg matrix because of two or more consecutive small
subdiagonal elements.
- S (local input/output) REAL array, (LDS,*)
- On entry, the matrix of shifts. Only the 2x2 diagonal of S is referenced.
It is assumed that S has JBLK double shifts (size 2). On exit, the data is
rearranged in the best order for applying.
- LDS (local input) INTEGER
- On entry, the leading dimension of S. Unchanged on exit. 1 < NBULGE
<= JBLK <= LDS/2
- NBULGE (local input/output) INTEGER
- On entry, the number of bulges to send through H ( >1 ). NBULGE should
be less than the maximum determined (JBLK). 1 < NBULGE <= JBLK <=
LDS/2 On exit, the maximum number of bulges that can be sent through.
- JBLK (local input) INTEGER
- On entry, the number of shifts determined for S. Unchanged on exit.
- H (local input/output) REAL array (LDH,N)
- On entry, the local matrix to apply the shifts on. H should be aligned so
that the starting row is 2. On exit, the data is destroyed.
- LDS (local input) INTEGER
- On entry, the leading dimension of S. Unchanged on exit.
- N (local input) INTEGER
- On entry, the size of H. If all the bulges are expected to go through, N
should be at least 4*NBULGE+2. Otherwise, NBULGE may be reduced by this
routine.
- ULP (local input) REAL
- On entry, machine precision Unchanged on exit.
Implemented by: G. Henry, May 1, 1997